It all depends on your character and the style of animation you want to do. Organic models, like living bodies, animal and humanoids, generally are single-mesh for the body, sometimes for the clothes & accessories too, depending on how you want them to move.
Lots of folks using Cloth sims to do clothing nowadays, usually requires a separate mesh that’s often a child of the armature, sometimes weighted to move with some of the bones as well. Separate non-Cloth clothing will also require weighting for armature motion.
Accessories can be made part of a single mesh but they will need to be weighted just like the body/clothes, and that can sometimes lead to odd distortions if not done just right.
Rigid-jointed & limbed characters like robots (or other mechanical devices) are often collections of separate meshes parented individually to bones in the rig rather than to the armature as a whole. They follow the parent bone motion as if all verts were weighted 1.0 to that bone (though no weighting is actually needed).
I think it’s most often wise to parent to the armature, though in some cases (like a pin on a lapel, or buttons on a Cloth mesh), parenting to groups pf vertices in the mesh works great: http://blenderartists.org/forum/showthread.php?t=181744
So you can see there’s no stone-carved solution, and a lot depends on your character, your rig, and what you intend to do with it.